How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I ?

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Solution

MADHUBANI

Total number of words that ends with letter I= $\frac{8!}{2!}$

= $8 \times 7 \times 5 \times 6 \times 4 \times 3$

= $56 \times 30 \times 12$

= 20160

If the words starts with M and end with I, there are 7 space left for 7 letters

Number of words that starts with M and end with I = $\frac{7!}{2!}$

= $7 \times 5 \times 4 \times 3$

= $42 \times 60$

= 2520

Number of words which do not start with M but end with 1= 20160-2520

Required number of words = 17460

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